 | Mathematical association - 1883 - 86 pages
...given points is the straight line that bisects at right angles the line joining those points. THEOR. 9. A straight line cannot meet the circumference of a circle in more than two points. COR. A chord of a circle lies wholly within the circle. OBS. Hence the circumference of a circle is... | |
 | Edward John Hamilton - Psychology - 1883 - 738 pages
...of contradiction. Many geometrical theorems have been demonstrated in this way. The proposition that "A straight line cannot meet the circumference of a circle in more than two points," is proved as follows: " For, if it could meet it in three, those three points would be equally distant... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...than OB ; /. 15. and in like manner any point in CE, except C, is without the circumference. QED COR. A straight line cannot meet the circumference of a circle in more than two points. DEF. 8. A secant is a straight line of unlimited length which meets the circumference of a circle in... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...circumferences will coincide, since all the points of both are at the same distance from the centre (179). (3) A straight line cannot meet the circumference of a...than two points. For, if it could meet it in three points, theso three points would be equally distant from the centre (179). There would then be three... | |
 | Edward John Hamilton - Logic - 1891 - 348 pages
...assertion true. For any antecedent which necessitates a false consequent must itself be false. That a straight line cannot meet the circumference of a circle in more than two points is proved as follows. "For if it could meet it in three or more points, all those points would be equally... | |
 | Edward John Hamilton - Logic - 1891 - 352 pages
...more than two points is proved as follows. "For if it could meet it in three or more points, all those points would be equally distant from the centre, and hence there would be three or more equal straight lines drawn from the same point to the same straight line. But this is impossible.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...will coincide with the arc APB; because every point in each is equally distant from the centre O. 143. A straight line cannot meet the circumference of a...than two points. For if it could meet it in three points, these three points would be equally distant from the centre (127). There would then be three... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...concentric, if they have the same centre. ARCS, CHORDS, AND TANGENTS. PROPOSITION I. THEOREM. 235. A straight line cannot meet the circumference of a circle in more than two points. F Let HK be any line meeting the circumference HKM in H and K. To prove that HK cannot meet the circumference... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...concentric, if they have the same centre. ARCS, CHORDS, AND TANGENTS. PROPOSITION I. THEOREM. 235. A straight line cannot meet the circumference of a circle in more than two points. v Let HK be any line meeting the circumference HKM in H and K. To prove that HK cannot meet the circumference... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...concentric, if they have the same, centre. ARCS, CHORDS, AND TANGENTS. PROPOSITION I. THEOREM. 235. A straight line cannot meet the circumference of a circle in more than two points. p Let HK be any line meeting the circumference HKM in H and K. To prove that HK cannot meet the circumference... | |
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THEOREM. A straight line cannot meet the circumference of a circle in more than two points. 
